Signaled by nonanalyticities in the time evolution of physical observables, dynamic quantum phase transitions (DQPTs) emerge in quench dynamics of topological systems and possess an interesting geometric origin captured by dynamic topological order parameters (DTOPs). In this Letter, we report the experimental study of DQPTs using discrete-time quantum walks of single photons. We simulate quench dynamics between distinct Floquet topological phases using quantum-walk dynamics and experimentally characterize DQPTs and the underlying DTOPs through interference-based measurements. The versatile photonic quantum-walk platform further allows us to experimentally investigate DQPTs for mixed states and in parity-time-symmetric nonunitary dynamics for the first time. Our experiment directly confirms the relation between DQPTs and DTOPs in quench dynamics of topological systems and opens up the avenue of simulating emergent topological phenomena using discrete-time quantum-walk dynamics.

Parity-time ($PT$)-symmetric Hamiltonians have widespread significance in non-Hermitian physics. A $PT$-symmetric Hamiltonian can exhibit distinct phases with either real or complex eigenspectrum, while the transition points in between, the so-called exceptional points, give rise to a host of critical behaviors that holds great promise for applications. For spatially periodic non-Hermitian systems, $PT$ symmetries are commonly characterized and observed in line with the Bloch band theory, with exceptional points dwelling in the Brillouin zone. Here, in nonunitary quantum walks of single photons, we uncover a novel family of exceptional points beyond this common wisdom. These “non-Bloch exceptional points” originate from the accumulation of bulk eigenstates near boundaries, known as the non-Hermitian skin effect, and inhabit a generalized Brillouin zone. Our finding opens the avenue toward a generalized $PT$-symmetry framework, and reveals the intriguing interplay between $PT$ symmetry and non-Hermitian skin effect.

We experimentally simulate nonunitary quantum dynamics using a single-photon interferometric network and study the information flow between a parity-time- ($\mathcal{P}\mathcal{T}$-)symmetric non-Hermitian system and its environment. We observe oscillations of quantum-state distinguishability and complete information retrieval in the $\mathcal{P}\mathcal{T}$-symmetry-unbroken regime. We then characterize in detail critical phenomena of the information flow near the exceptional point separating the $\mathcal{P}\mathcal{T}$-unbroken and $\mathcal{P}\mathcal{T}$-broken regimes, and demonstrate power-law behavior in key quantities such as the distinguishability and the recurrence time. We also reveal how the critical phenomena are affected by symmetry and initial conditions. Finally, introducing an ancilla as an environment and probing quantum entanglement between the system and the environment, we confirm that the observed information retrieval is induced by a finite-dimensional entanglement partner in the environment. Our work constitutes the first experimental characterization of critical phenomena in $\mathcal{P}\mathcal{T}$-symmetric nonunitary quantum dynamics.

We report the experimental detection of bulk topological invariants in nonunitary discrete-time quantum walks with single photons. The nonunitarity of the quantum dynamics is enforced by periodically performing partial measurements on the polarization of the walker photon, which effectively introduces loss to the dynamics. The topological invariant of the nonunitary quantum walk is manifested in the quantized average displacement of the walker, which is probed by monitoring the photon loss. We confirm the topological properties of the system by observing localized edge states at the boundary of regions with different topological invariants. We further demonstrate the robustness of both the topological properties and the measurement scheme of the topological invariants against disorder.